Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework.

Area of Science:

• Robotics
• Artificial Intelligence
• Computational Mathematics

Background:

• Harmonic functions, like the Poisson equation, offer powerful properties for autonomous navigation.
• Traditional numerical methods for solving these equations are computationally expensive, hindering real-time applications.
• This limits the practical use of harmonic functions in mobile robot path planning.

Purpose of the Study:

• To present a novel real-time global path planning method for mobile robots.
• To overcome the computational limitations of traditional methods for harmonic function-based navigation.
• To enable efficient path generation even with dynamic changes in robot position or goal.

Main Methods:

• Utilizes Proper Generalized Decomposition (PGD) for the off-line generation of a comprehensive path set (computational vademecum).
• Applies harmonic potential fields to create the path database for a given environment.
• Implements the PGD-vademecum for on-line decision-making in path planning.

Main Results:

• The PGD-based method achieves negligible computational cost for real-time path planning.
• Demonstrated feasibility through simulated scenarios (L-shaped corridor, bug trap) and real-world experiments.
• Successfully navigated a LEGO MINDSTORMS robot in static environments with changing start/goal configurations.

Conclusions:

• Proper Generalized Decomposition (PGD) effectively enables real-time path planning using harmonic functions.
• The PGD-vademecum approach is computationally efficient and suitable for resource-constrained robots.
• This method holds potential for advancing autonomous navigation in social robots and other applications.